How do I merge these individual components into one solid object?
These small rectangles are called faces. It's the surface of your solid object. There is nothing wrong with them and there is no need to merge them. That's normal. The objects are shown in the Outliner in top right of the screeen.
If you're new to Blender I recommend to watch video like this 3D for NOOBS - Livestream Lesson 01. It explains 3D stuff and Blender's interface and basics. It's for absolute beginners.